# [gmx-users] No convergence in Diffusion Coefficient

David van der Spoel spoel at xray.bmc.uu.se
Tue Jun 29 06:57:19 CEST 2010

```On 2010-06-29 05.50, Igor Leontyev wrote:
> See the table bellow, there is no convergence of the Self-Diffusion
> Coefficient (Dself) over the trajectory length. Dself is obtained for NPT
> box of 1024 SPC/E water molecules by the Einstein's relation (via RMSD). In
> Gromacs Manual or Alien&Tildesley's book I didn't find issues related to
> the
> problem. Is there any idea why I can not achieve the convergence?
>
> Description:
> To figure out what the trajectory length is needed for an accurate
> simulation of the self-diffusion coefficient I performed the following
> test.
> Split the continuous 10ns long trajectory on parts and calculated Dself for
> each of the parts, e.g. the splitting on N parts gives N values of Dself
> obtained on trjlenth=10ns/N trajectory part. For the variety of N values we
> can calculate the average <Dself> and dispersion Disper. The converged
> trajectory length is found as the trjlenth value at which the dispersion is
> sufficiently small and <Dself> equal to the value obtained for the whole
> 10ns trajectory. But it turned out that Dself does not converge (See the
> columns 3 and 4 in the Table).
>
> Just for the comparison I carried out the same test for the Dielectric
> Constant Eps (See the columns 5 and 6 in the Table) and the converged
> trajectory length is about 2.5-5ns which correlates with the length
> reported
> in the literature.

You don't say how you compute the Dself. Your Dself varies from 2.48 to
2.63, and if you drop the 10 ns and 4.8 ps measurements it varies from
2.48 to 2.54. Not too much I would say.

g_msd tries to do something semi-intelligent, by fitting the MSD to a
straight line from 10 to 90% of the length of the graph. You should
avoid using the very first few ps and the final bit of the graph.

Another way of getting statistics is by spitting the system in 2-N
sub-boxes and computing the Dself for each of these.

>
> ------------------------------------------------------------
> trjlenth N <Dself> Disper <Eps> Disper
> ps 1e-5 cm^2/s
> ------------------------------------------------------------
> 10000.0 1 2.6305 0 72.0 0
> 5000.0 2 2.4591 .0929 71.9 1.1
> 2500.0 4 2.4554 .0291 71.6 4.7
> 1250.0 8 2.4816 .0618 71.1 5.2
> 625.0 16 2.4848 .0786 70.6 7.5
> 312.5 32 2.4993 .0848 67.7 9.4
> 156.2 64 2.5128 .1082 63.3 11.6
> 78.1 128 2.4993 .1119 56.3 14.1
> 39.0 256 2.5072 .1303 43.6 14.9
> 19.5 512 2.5133 .1713 31.0 12.4
> 9.7 1030 2.5449 .2128 19.6 8.0
> 4.8 2083 2.6318 .2373 12.0 4.9
>
>

--
David van der Spoel, Ph.D., Professor of Biology
Dept. of Cell & Molec. Biol., Uppsala University.
Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205.
spoel at xray.bmc.uu.se    http://folding.bmc.uu.se

```